Optical scanner and image forming apparatus

ABSTRACT

An optical scanner includes a single deflector to optically scan a plurality of target surfaces. The deflector is shared by all the beams from a plurality of light sources. The optical scanner includes photodetectors arranged to receive the deflected beams deflected. The beams traveling toward the deflector have an open angle in a deflecting rotation plane. A plurality of scanning optical systems are arranged to guide the deflected beams to different target surfaces. Each of the scanning optical systems includes at least two identical scanning lenses. At least one specific scanning lens in the scanning optical system is at a position rotated 180 degrees from a corresponding specific scanning lens in another scanning optical system. The specific scanning lens has a sub scan curvature on at least one surface with a shape asymmetrically varying from an optical axis toward both peripheries in the main scan direction.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Division of and claims the benefit of priorityunder 35 U.S.C. §120 from U.S. Ser. No. 10/787,095, filed Feb. 27, 2004,and claims the benefit of priority under 35 U.S.C. §119 from JapanesePatent Applications Nos. 2003-051428, filed Feb. 27, 2003, and2003-369231, filed Oct. 29, 2003, the entire contents of each which areincorporated herein by reference.

BACKGROUND OF THE INVENTION

1) Field of the Invention

The present invention relates to an optical scanner and an image formingapparatus.

2) Description of the Related Art

An optical scanner may employ a single deflector to optically scanplural target surfaces. The optical scanner is used in an image formingdevice to form a color image as is known in the art. When such opticalscan mode is applied to a color image forming device, it is not requiredto use the deflector more than one. In this case, the number of plurallight sources required is equal to or more than that of the targetsurfaces (the number equal to that of the target surfaces in a singlebeam scan mode, and the number equal to or more than that of the targetsurfaces in a multi-beam scan mode). In addition, as the light sourcesare arranged separately, the number of components for light sourcearrangement increases. When environmental fluctuations and the likecause relative variations in optical scanning with beams from the lightsources, the variations raise a phenomenon called “out-of-colorregistration”, which deteriorates the image quality in a color image tobe formed.

Proposed as a configuration of the above optical scanner is a “systemthat passes plural beams traveling toward different target surface”through a scanning lens proximate to the deflector (see Japanese PatentApplication Laid-Open No. 2001-4948).

This optical scanner can reduce the out-of-color registration due to theenvironmental variation because plural beams traveling toward differenttarget surfaces pass through the same scanning lens. In this case,however, plural beams traveling toward the deflector have no open anglein a deflecting rotation plane. Therefore, it is required to locate anadditional optical path deflector such as a prism before the deflector,which increases the number of components and easily invitescost-elevation. The optical path deflector, for example, the prismeasily causes a deteriorated optical characteristic and a reducedutilization efficiency of light.

In the conventional color image forming device, “photodetectorsoperative to receive deflected beams” for use in timing control ofoptical scanning are arranged individually as corresponding to differenttarget surfaces. This arrangement invites an increase in the number ofcomponents and cost-elevation. In addition, if relative arrangements ofthe photodetectors fluctuate due to environmental variations, initialpositions of optical scanning in the target surfaces may be changedrelatively to cause the out-of-color registration in a color image to beformed.

In recent years, for achievement of color digital copiers and colorlaser printers with higher recording speeds, different colored-imagesare formed on plural target surfaces. These images are then sequentiallytransferred onto a recording medium to complete a color image. Suchdevices have been known widely as so-called “tandem type color imageforming devices”.

Proposed as such the tandem type color image forming device is anoptical scanner that includes a single deflector sandwiched betweenscanning optical systems arranged at both sides thereof to opticallyscan four photosensitive members at the same time (see Japanese PatentApplication Laid-Open No. 2002-90672).

The higher the image quality of color images to be formed, the more thereduction of light spot diameters proceeds. In order to reduce a lightspot diameter, another proposal is given to a scanning lens. Thisscanning lens employs a special toric surface, which has the varyingradius of a sub scan curvature from the optical axis of the lens surfaceto peripheries in the main scan direction (see Japanese PatentApplication Laid-Open No. 2001-324689).

In the tandem type color image forming device disclosed in JapanesePatent Application Laid-Open No. 2002-90672, beams from a plurality oflight sources enter a light deflector while having an “open angle” in adeflecting rotation plane toward the light deflector. Therefore, theyhave different average incident angles to the optical axis of thescanning optical system, resulting in a sag-effected deterioration ofoptical characteristics, particularly curvature of the image plane inthe sub scan direction, which makes it difficult to reduce light spotdiameters.

SUMMARY OF THE INVENTION

It is an object of the present invention to at least solve the problemsin the conventional technology.

An optical scanner according to one aspect of the present inventionincludes a plurality of light sources; a coupling optical systemarranged to couple beams emitted from the light sources; a line imagefocusing optical system arranged to focus each beam coupled to a lineimage extending longer in a main scan direction; a deflector that hasdeflecting reflective surfaces on focused positions of the line imageand a common rotary axis for the deflecting reflective surfaces, isshared for all the beams from the light sources, and deflects the beamsfocused; a scanning optical system arranged to guide the beams deflectedto a plurality of target surfaces for optical scanning; and aphotodetector arranged to receive the beams deflected at the deflector.The beams traveling toward the deflector have an open angle θ in adeflecting rotation plane. The scanning optical system includes at leasttwo scanning lenses. A scanning lens proximate to the target surface,out of the scanning lenses, passes only the beams traveling toward asame target surface. Scanning lenses proximate to the target surfacesfor guiding the beams to different target surfaces have optical actionsdifferent from each other.

An image forming apparatus according to another aspect of the presentinvention includes the optical scanner according to the presentinvention.

The other objects, features, and advantages of the present invention arespecifically set forth in or will become apparent from the followingdetailed descriptions of the invention when read in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustrative view of one embodiment of the optical scanneraccording to the present invention;

FIG. 2 is a schematic view illustrating an optical arrangement of theoptical scanner of FIG. 1 seen from the main scan direction;

FIGS. 3A and 3B are illustrations of problems associated with beamsentering a common deflector from plural light sources when they have noopen angle in a deflecting rotation plane;

FIGS. 4A to 4C are illustrations of an effect on a given open angle;

FIG. 5 is an illustration of a single photodetector operative to receivea light spot composed of beams emitted from different light sources andgiven an open angle;

FIGS. 6A and 6B are illustrative views of another embodiment of theoptical scanner according to the present invention;

FIG. 6C is a schematic view illustrating an optical arrangement of theoptical scanner of FIG. 6A seen from the main scan direction;

FIG. 7 is an illustration of the reduction of the beam width in the subscan direction;

FIG. 8 is an illustration of the enlargement of the spacing betweendifferent beams in the sub scan direction;

FIG. 9 illustrates one embodiment of an image forming apparatusaccording to the present invention;

FIG. 10 illustrates another embodiment of an optical scanner accordingto the present invention;

FIGS. 11A and 11B illustrate image surface curvatures in A and A′optical systems according to Example I;

FIG. 12 illustrates an image surface curvature in A′ (B′) opticalsystem, which is corrected well together with the image surfacecurvature in A (B) optical system shown in FIGS. 11A and 11B;

FIGS. 13A and 13B illustrate image surface curvatures in A and D opticalsystems according to Example III;

FIGS. 14A and 14B illustrate image surface curvatures with the incidentangle of 58 degrees;

FIGS. 15A and 15B illustrate image surface curvatures with the incidentangle of 73 degrees;

FIGS. 16A and 16B illustrate image surface curvatures with the incidentangle of 73 degrees and the scanning lens 206A′ arranged as rotated 180degrees around the optical axis;

FIGS. 17A and 17B are diagrams illustrating variations in spot diameterwith the incident angle of 58 degrees in the main scan direction due todefocus according to Example V;

FIGS. 18A and 18B are diagrams illustrating variations in spot diameterwith the incident angle of 73 degrees in the main scan direction due todefocus according to Example V;

FIG. 19 is a diagram illustrating power in the sub scan direction of thescanning lens in Example V;

FIG. 20 is a diagram illustrating power in the sub scan direction ofanother scanning lens in Example V;

FIG. 21 is a diagram illustrating variations in sub scan curvature inthe main scan direction on a first surface of the scanning lens inExample V; and

FIG. 22 is a diagram illustrating variations in sub scan curvature inthe main scan direction on a first surface of another scanning lens inExample V.

DETAILED DESCRIPTION

Exemplary embodiments of an optical scanner and an image formingapparatus relating to the present invention will be explained in detailbelow with reference to the accompanying drawings.

FIG. 1 is an illustration of one embodiment of an optical scanneraccording to the present invention.

As for optical paths extending from a polygon mirror (i.e. deflector) 4to target surfaces (i.e. photosensitive objects) 8A, 8A′, 8B, and 8B′ tobe scanned, they are shown as developed in the same plane for theconvenience of depiction. The plane of the drawing sheet corresponds toa deflecting rotation plane, which is a virtual plane perpendicular tothe common rotary axis of the polygon mirror.

Semiconductor lasers (i.e. light sources) 1A, 1A′, 1B, and 1B′ emitdivergent beams, which are converted into collimated beams (or weaklyconverged beams or weakly diverged beams) through coupling opticalsystems including coupling lenses 2A, 2A′, 2B, and 2B′. The convertedbeams are then subjected to shaping into desired beam sections whilepassing through apertures 14A, 14A′, 14B, and 14B′ for forming desiredspot diameters on the target surfaces. The shaped beams then enter lineimage optical systems including cylindrical lenses 3A, 3A′, 3B, and 3B′having powers only in the sub scan direction.

The semiconductor lasers 1A, 1A′, 1B, and 1B′ correspond to therespective target surfaces one by one. If there are N target surfaces,there are N semiconductor lasers (light sources) correspondingly where Ndenotes an integer equal to 2 or more. The optical scanning may beperformed in either a single beam mode or a multi-beam mode.

Each semiconductor laser may emit M (≧1) beams to optically scan eachtarget surface with M beams. When M≧2, each semiconductor laser may be asemiconductor laser array that emits M beams. Alternatively, it may be asystem that includes a light synthesis prism operative to synthesizebeams emitted from M semiconductor lasers.

The beams emitted from the semiconductor lasers 1A and 1A′ have an openangle θ in the deflecting rotation plane and a certain spacing in thesub scan direction (the direction perpendicular to the drawing sheet)therebetween. In other words, when the beams traveling toward thepolygon mirror 4 are projected onto the deflecting rotation plane fromthe direction along the common rotary axis of the polygon mirror 4,projections of the beams are mutually laid open “at an angle θ from thepolygon mirror 4 to the semiconductor lasers 1A and 1A′. Similarly, thebeams emitted from the semiconductor lasers 1B and 1B′ have an openangle θ in the deflecting rotation plane and a certain spacing in thesub scan direction (the direction perpendicular to the drawing sheet)therebetween.

The cylindrical lenses 3A, 3A′, 3B, and 3B′ are arranged to cause theincoming beams to be condensed in the sub scan direction and focused toline images extending longer in the main direction on the polygon mirror4 in the vicinity of deflecting reflective surfaces thereof. When thebeams are reflected at the polygon mirror 4, they are converted intodeflected beams that deflect at a constant angular velocity as thepolygon mirror 4 rotates at a constant velocity.

The beam emitted from the semiconductor laser 1A passes through scanninglenses 5A and 6A and a dust-tight glass member 7A while deflecting andreaches as a condensed light spot onto the target surface 8A foroptically scanning the target surface 8A. The beam emitted from thesemiconductor laser 1A′ passes through scanning lenses 5A′ and 6A′ and adust-tight glass member 7A′ while deflecting and reaches as a condensedlight spot onto the target surface 8A′ for optically scanning the targetsurface 8A′.

The beam emitted from the semiconductor laser 1B passes through scanninglenses 5B and 6B and a dust-tight glass member 7B while deflecting andreaches as a condensed light spot onto the target surface 8B foroptically scanning the target surface 8B. The beam emitted from thesemiconductor laser 1B′ passes through scanning lenses 5B′ and 6B′ and adust-tight glass member 7B′ while deflecting and reaches as a condensedlight spot onto the target surface 8B′ for optically scanning the targetsurface 8B′.

Prior to optical scanning of the target surfaces 8A and 8A′, the beamsfrom the semiconductor lasers 1A and 1A′ are detected at a photodetector11 through a mirror 9 and a lens 10, for adjustment of synchronizationassociated with the start of optical writing. Similarly, prior tooptical scanning of the target surfaces 8B and 8B′, the beams from thesemiconductor lasers 1B and 1B′ are detected at a photodetector 14through a mirror 12 and a lens 13, for adjustment of synchronizationassociated with the start of optical writing.

FIG. 2 is a diagram viewed from the main scan direction of the opticalarrangement shown in FIG. 1. The target surfaces 8A to 8B′ arepractically found on photoconductive photosensitive media orphotosensitive drums. The optical paths in the beams for opticalscanning of these photosensitive drums 8A to 8B′ are turned by mirrorsMa, Ma′1, Ma′2, Mb1, Mb2, and Mb′ as shown.

The effect on the given open angle θ in the deflecting rotation plane isexplained below.

FIGS. 3A and 3B illustrate comparative examples. FIG. 3A illustrates aprojection on the deflecting rotation plane. As shown in FIG. 3A, seenfrom the projection on the deflecting rotation plane, the beam emittedfrom the semiconductor laser 1A′ is coupled through the coupling lens2A′. The coupled beams is then turned at optical path deflectors 31 and32 so as to have the optical path matched with the optical path of thebeam emitted from the semiconductor laser 1A and coupled through thecoupling lens 2A.

FIG. 3B illustrates the optical paths of the beams from thesemiconductor lasers 1A and 1A′ with the vertical direction viewed asthe sub scan direction.

The semiconductor lasers 1A and 1A′ are driven for modulation based onimage signals. The semiconductor lasers may have a fluctuation in outputwhen a return ghost light enters.

As shown in FIG. 3A, the cylindrical lens 3A, 3A′ may reflect the beam.In this case, the beams from the semiconductor lasers 1A and 1A′ have noopen angle in the deflecting rotation plane. Thus, the beam, forexample, emitted from the semiconductor laser 1A and reflected at thecylindrical lens 3A may enter the semiconductor laser 1A′ as a returnghost light (as shown with the dotted line in FIG. 3B). This returnghost light causes a fluctuation in output from the semiconductor laser1A′. Similarly, when the beam from the semiconductor laser 1A isreflected at the cylindrical lens 3A′, the reflected beam enters thesemiconductor laser 1A as a return ghost light to cause a fluctuation inoutput from the semiconductor laser 1A. Such fluctuations in output fromthe semiconductor laser cause density variations in a color image.

If the beams from the semiconductor lasers 1A and 1A′ have the openangle θ in the deflecting rotation plane as in the optical scanner ofFIG. 1, the return ghost light reflected from the cylindrical lens cannot enter the other semiconductor laser. This is effective to stabilizethe output from the semiconductor laser.

FIGS. 4A to 4C exemplify the semiconductor lasers 1A and 1A′ and thecoupling lenses 2A and 2A′ for coupling the lights emitted from theselasers in the embodiment shown in FIG. 1, which are integrated into aunit.

FIG. 4A is a cross-sectional view of the united light source in thedeflecting rotation plane, and FIG. 4B is a view seen from the directionalong the optical axis. The semiconductor lasers 1A and 1A′ and thecoupling lenses 2A and 2A′ are mounted and integrated on a base member40.

The coupling lenses 2A and 2A′ are fixedly adhered on the base member 40via an adhesive layer of an ultraviolet curing resin.

If the beams from the semiconductor lasers 1A and 1A′ have the openangle θ in the deflecting rotation plane, it is possible to reduce aspacing in the sub scan direction (L1) between the beams from plurallight sources corresponding to different target surfaces as shown inFIG. 4B. This is effective to integrate the light sources into a unit.

A method of uniting the semiconductor lasers 1A and 1A′ can beconsidered as to include arranging the semiconductor lasers and thecoupling lenses in the sub scan direction on a base member 40′ as shownin FIG. 4C. In this case, however, the polygon mirror is given a largerheight because the spacing between the beams in the sub scan direction,L1′, increases.

As shown in FIGS. 4A and 4B, at least two semiconductor lasers 1A and1A′ each for different target surfaces may be mounted and integrated onthe base member 40. This is effective to decrease the number ofcomponents, suppress relative dot positional fluctuations on the targetsurfaces due to plural semiconductor lasers 1A and 1A′, and reduce theout-of-color registration.

In the embodiment shown in FIG. 1, prior to optical scanning of thetarget surfaces 8A and 8A′, the beams emitted from the semiconductorlasers 1A and 1A′ are received and detected at the photodetector 11.Similarly, prior to optical scanning of the target surfaces 8B and 8B′,the beams emitted from the semiconductor lasers 1B and 1B′ are receivedand detected at the photodetector 14.

The beams from the semiconductor lasers 1A and 1A′ have the open angletherebetween. Therefore, when light spots of these beams pass throughthe position of the photodetector 11, the light spots SA and SA′ areseparated in the main scan direction as shown in FIG. 5. Thus, thesingle photodetector 11 can detect the light spots SA and SA′individually. Similarly, the beams from the semiconductor lasers 1B and1B′ can be detected individually at the single photodetector 14.

The use of such a common photodetector operative to detect plural beamsfor optical scanning of different target surfaces causes no deviationsin relative start positions of writing on the target surfaces 8A and 8A′and relative start positions of writing on the target surfaces 8B and8B′. This is effective to reduce the out-of-color registration in acolor image to be formed.

The establishment of the open angle θ yields the above advantages. Inthe presence of the open angle, however, the sag on the polygon mirror 4(variations in reflection points) has the effect of causing a relativesub scan image surface curvature between the beams corresponding todifferent target surfaces, resulting in growth of the spot diameter inthe sub scan direction.

In the embodiment shown in FIGS. 1 and 2, the scanning optical systemincludes two scanning lenses 5A and 6A to solve the problem. Inaddition, the scanning lenses 6A, 6A′, 6B, and 6B′ proximate to thetarget surfaces have different optical characteristics from each other.This is effective to reduce the relative sub scan image surfacecurvature between the beams corresponding to different target surfacesand achieve a small and stable spot diameter.

In the embodiment described above, as shown in FIG. 2, the scanninglenses 5A and 5A′ are integrated with the scanning lenses 5B and 5B′though they may be separated from each other.

A difference in sag between plural beams caused on the polygon mirror 4may be denote with A. Using this A and a lateral power β of the opticalsystem between the deflecting reflective surface and the target surfacein the sub scan direction, a difference in relative sub scan imagesurface curvature can be represented by: β²×Δ.

Accordingly, the less the lateral power β, the more the relative subscan image surface curvature between different target surfaces can bereduced. Preferably, to reduce the lateral power β, the optical scanninglenses 6A to 6B′ proximate to the target surfaces have larger powers inthe sub scan direction compared to powers in the sub scan direction ofthe optical scanning lenses 5A to 5B′ proximate to the polygon mirror 4.

If the scanning optical system is made as a reducing optical system(1<|β|), the “relative sub scan image surface curvature” can be reducedcompared to the sag difference Δ. This is effective to achieve a smalland stable spot diameter.

The scanning lenses 6A, 6A′ and the scanning lenses 6B, 6B′ proximate tothe target surfaces for guiding the beams to different target surfacesmay have different shapes from each other. The scanning lenses 6A, 6A′and the scanning lenses 6B, 6B′ may also have different arrangementformations from each other even if the scanning lenses have the sameshape. This is effective to reduce the relative sub scan image surfacecurvature associated with different target surfaces and achieve a smalland stable spot diameter.

In each of the scanning lenses 6A to 6B′ proximate to the targetsurfaces, a radius of curvature in the sub scan direction on at leastone surface may asymmetrically vary gradually from an optical axistoward both peripheries. This is effective to suppress an absolute subscan image surface curvature to a desired amount in every target surfaceeven if a relative sub scan image surface curvature arises amongdifferent target surfaces. This is also effective to achieve a small andstable spot diameter.

FIGS. 6A, 6B, and 6C illustrate another embodiment of the opticalscanner. FIG. 6A illustrates a state of the optical scanner projectedonto a deflecting rotation plane. FIG. 9B illustrates a state of theoptical scanner seen from the main scan direction developing opticalpaths linearly. FIG. 6C is a schematic view illustrating an opticalarrangement of the optical scanner of FIG. 6A seen from the main scandirection.

Semiconductor lasers (light sources) 101A, 101B, 101C, and 101D emitbeams, which pass through coupling lenses (constituting a couplingoptical system) 102A, 102B, 102C, and 102D, apertures 114A, 114B, 114C,and 114D and cylindrical lenses (constituting a line image focusingoptical system) 103A, 103B, 103C, and 103D toward a polygon mirror (i.e.deflector) 104. The reference symbol DM denotes a dummy mirror, whichmay be omitted. Four beams deflected at the polygon mirror 104 with asingle rotary axis are guided through scanning optical systems to thecorresponding target surfaces 108A to 108D.

Each of the scanning optical systems corresponding to the targetsurfaces includes two scanning lenses. Of these two scanning lenses, thescanning lens 105 proximate to the polygon mirror 104 is shared by allbeams for optical scanning of the target surfaces 108A to 108D, and thescanning lens proximate to the target surface is one of individualscanning lenses 106A to 106D.

As outlined in FIG. 6B, the four beams deflected at the polygon mirror104 commonly pass through a lens surface of the scanning lens 105 andindividually pass through the respective scanning lenses 106A to 106D toreach the respective target surfaces 108A to 108D as focused light spotsfor optical scanning.

The scanning lens 105 has a constant velocity corrective function. Thescanning lens 105 is shared by plural beams that travel toward differenttarget surfaces. This is effective to decrease the number of componentsand reduce relative dot positional deviations in the main scan directionon different target surfaces due to process variations and temperaturedistributions on the scanning lens 105.

The four incident beams to the polygon mirror 104 from the semiconductorlasers 101A to 101D have an open angle θ in the deflecting rotationplane as shown. The open angle θ has the effect described earlier.

The scanning lens 105 proximate to the polygon mirror 104, arranged topass the four beams traveling toward different target surfaces 108A to108D, has a power Pm in the main scan direction and a power Ps in thesub scan direction, which satisfy the following condition:Pm>0≧Ps

The effect under condition of 0≧Ps is explained with reference to FIGS.7 and 8.

The optical system shown in FIGS. 6A and 6B has a large subjectassociated with separation of beams. Easy separation of plural deflectedbeams from each other at the image side about the scanning lens 105requires reduction of the beam width in the sub scan direction andenlargement of the spacing between different beams in the sub scandirection.

FIG. 7 is an illustration of the reduction of the beam width in the subscan direction. FIG. 8 is an illustration view of the enlargement of thespacing between different beams in the sub scan direction.

In FIG. 7, the chain lines indicate the case of 0=Ps, the dotted linesindicate the case of 0>Ps, and the solid lines indicate the case ofPs>0.

A spot diameter in the sub scan direction on the target surface isdetermined with an open angle φ in the sub scan direction of the beamtraveling toward the target surface. The larger the open angle φ, themore the spot diameter can be reduced.

In other words, the open angle φ is required unchanged to achieve thesame spot diameter at the same wavelength.

In the optical system shown in FIGS. 6A and 6B, the scanning lens 105has a “positive power in the sub scan direction” in the art. In thiscase, however, as shown with the solid lines in FIG. 7, the beam widthexpands in the sub scan direction before the scanning lens 106A,resulting in difficult separation of beams.

If Ps=0, the beam is not refracted in the sub scan direction through thescanning lens 105 (the chain lines). Therefore, the beam width isreduced in the sub scan direction at the incident side about thescanning lens 105, resulting in easy separation of beams. If 0>Ps, thebeam diameter is further reduced in the sub scan direction at theincident side about the scanning lens 106 (the dotted lines).

FIG. 8 illustrates a difference in spacing between two beams (FL1, FL2)due to a difference in “power in the sub scan direction” of the scanninglens 105. As shown in the figure, if Ps>0, the spacing between the beamsFL1 and FL2 behind the scanning lens 105 is narrowed as indicated withthe chain lines. To the contrary, if 0>Ps (the solid lines and dottedlines), the spacing between the beams FL1 and FL2 is expanded, resultingin easy separation of beams.

As described above, the scanning lens 5 proximate to the polygon mirror104 has a positive power in the main scan direction (Pm>0). In addition,most of functions for correction of the focusing property and correctionof the constant velocity property in the main scan direction on thetarget surfaces 108A to 108D is imparted on the scanning lens 105. Thisis effective to downsize the scanning optical system.

It is possible under condition of 0>Ps to perform easy separation ofbeams, downsize the polygon mirror 104, and achieve reduced powerconsumption, increased durability and lowered noises. It is alsopossible to downsize the scanning lens 105 proximate to the polygonmirror 104.

It is possible under condition of 0>Ps to lower the absolute value ofthe lateral power in the sub scan direction of the scanning opticalsystem, reduce the sub scan image surface curvature, and achieve adownsized and stabilized spot diameter.

The scanning lenses 106A to 106D proximate to the target surfaces areemployed to pass only the beams traveling toward the same target surfaceto achieve an easy optical layout.

If the scanning lens 105 proximate to the polygon mirror 104 is given apower of zero in the sub scan direction, it can reduce the dotpositional deviations in the main scan on different target surfaces.

If the scanning lens 105 proximate to the polygon mirror is arranged topass plural beams for optical scanning of different target surfaces 108Ato 108D, it is possible to reduced the relative dot positionaldeviations in the main scan direction due to temperature variations. Thescanning lens 105 proximate to the polygon mirror 104 is not required toinclude a single lens if it is integrated. For example, it may be formedby a method of integration molding or lamination.

FIG. 6C also illustrates a state of optical paths extending from thepolygon mirror 104 to the target surfaces 108A to 108D (photosensitivedrums) seen from the main scan direction. The reference symbols m1 to m8denote mirrors for optical path bending.

In the embodiments shown in FIGS. 1 and 6A, the beams emitted fromplural light sources are spatially separated along the path from thelight source to the line image optical system. Therefore, it is possibleto provide an optical scanner having a decreased number of componentsand reduced relative dot positional deviations among different targetsurfaces in spite of temperature variations without any optical pathdeflector.

FIG. 9 illustrates one embodiment of an image forming apparatusaccording to the present invention.

The image forming apparatus is an optical scanner-mounted, full-colortandem type image forming apparatus

A paper feed cassette 300 is located beneath the device and, above thecassette, a conveyer belt 330 is arranged to convey a recording sheet (asheet-like recording medium) S fed from the paper feed cassette 300.Above the conveyer belt 330, photosensitive drums 308Y, 308M, 308C, and308K (corresponding to the target surfaces 8A, 8A′, 8B, and 8B′ in FIG.2 and to the target surfaces 108A to 108D in FIG. 6C) are arrayed at anequal interval sequentially from the upstream side in the direction ofthe recording sheet conveyance.

The photosensitive drums 308Y, 308M, 308C, and 308K are formed to havethe same diameter and, around each of the drums, provided with a processunit for execution of xerographic processes. These process units havethe same array and operation for the photosensitive drums 308Y to 308K.Accordingly, the photosensitive drum 308Y is exemplified. In this case,a charging charger 314Y, a developing device 316Y, a transferringcharger 317Y, and a cleaner 318Y are arranged clockwise in this orderaround the photosensitive drum 308Y. The other photosensitive drums308M, 308C, and 308K also have the same arrangement.

An optical scanner 320 arranged above the array of the photosensitivedrums 308Y to 308K is of the type explained in FIGS. 1 and 2 or the typeexplained in FIGS. 6A and 6B, which optically scans the photosensitivedrums 308Y to 308K between the charging charger and the developingdevice.

Those arranged around the conveyer belt 330 include a resist roller 319and a belt charging charger 321 upstream to the photosensitive drum308Y, a belt separating charger 322 downstream from the photosensitivedrum 308K, and an erasing charger 323 and a cleaner 324 beneath thebelt.

Downstream from the belt separating charger 322 in the direction ofconveyance, fixing devices 325 are located to form a conveyance pathextending via paper ejection rollers 326 toward a paper ejection tray327.

In the full-color mode (multi-colored mode), the photosensitive drums308Y, 308M, 308C, and 308K are charged uniformly from the chargingchargers. Then, based on image signals having image components ofyellow, magenta, cyan, and black, optical scanning by the opticalscanner 320 forms electrostatic latent images corresponding to the imagecomponents on the drums.

These latent images are developed at the developing devices 316Y and thelike to visualize colored toner images of yellow, magenta, cyan, andblack.

The recording sheet S for carrying the color image is fed from the paperfeed cassette 300 and picked up onto the conveyer belt 330 through theresist roller 319 at controlled timing. The conveyer belt 330, chargedfrom the belt charging charger 321, attracts the recording sheet Sstatically. While the conveyer belt 330 conveys the recording sheet S,the charging charger 317Y transfers a yellow toner image from thephotosensitive drum 308Y to the recording sheet S.

Similarly, the charging chargers 317M, 317C, and 317K sequentiallytransfer toner images of magenta, cyan, and black from thephotosensitive drums 308M, 308C, and 308K to the recording sheet S.Thus, the four-colored toner images are superimposed on the recordingsheet S to form a color image thereon. After the toner images aretransferred, the photosensitive drums are cleaned at the cleaners 318Yand the like to remove residual toners and paper dusts.

The recording sheet S carrying the color image is separated from theconveyer belt 330 at the belt separating charger 322, passed through thefixing devices 325 to fix the color image, and ejected onto the paperejection tray 327 through the ejection rollers 326. After the recordingsheet S is separated, the conveyer belt 330 is erased by the erasingcharger 323 and cleaned by the cleaner 324.

In a black mode (monochromic mode), the image formation process is notperformed to the photosensitive drums 308Y, 308M, and 308C. Instead, theimage formation process is performed only to the photosensitive drum308K.

FIG. 10 illustrates another embodiment of an optical scanner accordingto the present invention.

Namely, the optical scanner in this embodiment including a plurality ofsemiconductor lasers (i.e. light sources) 201A and 201A′, one or morecoupling lenses (constituting a coupling optical system) 202A and 202A′arranged to couple beams emitted from the semiconductor lasers, one ormore cylindrical lenses (constituting line image focusing opticalsystems) 203A and 203A′ arranged to focus the beams coupled through thecoupling lenses to line images extending longer in the main scandirection, a polygon mirror (i.e. deflector) 204 having deflectingreflective surfaces in the vicinity of focused positions of the lineimages and arranged to deflect the beams from the cylindrical lenses,and a plurality of scanning lenses (constituting scanning opticalsystems) 205A, 205A′, 206A, and 206A′ arranged to guide the beamsdeflected at the polygon mirror 204 to different target surfaces to formfocused light spots.

The polygon mirror 204 has a common rotary axis for deflectingreflective surfaces. The beams entering a common deflecting reflectivesurface (either a single deflecting reflective surface or a plurality ofdeflecting reflective surfaces arrayed in the rotary axis direction inthe same plane) of the deflector to travel toward different targetsurfaces has an open angle (θ) in a deflecting rotation plane (in theplane of the drawing sheet).

Each of the scanning optical systems includes two or more scanninglenses and corresponding scanning lenses 205A and 205A′ and 206A and206A′ in the scanning optical systems are identical with each other. Atleast one scanning lens B (scanning lens 206A′) in the scanning opticalsystems arranged to guide the beams deflected at the common deflectingreflective surface to different target surfaces is located at a position180 degrees rotated about an optical axis from a corresponding scanninglens B (scanning lens 206A) in another scanning optical system. Thescanning lens B (scanning lens 206A′) has a sub scan curvature on atleast one surface with a shape asymmetrically varying gradually from anoptical axis toward both peripheries in the main scan direction.

Each semiconductor laser in the plurality of semiconductor lasercorresponds to the target surface one by one. Each semiconductor laseremits one or more beams. If each semiconductor laser emits one beam,each target surface is scanned in a single beam scan mode. If eachsemiconductor laser emits two or more beams, each target surface isscanned in a multi-beam scan mode.

If each semiconductor laser emits two or more beams, each semiconductorlaser may be a semiconductor laser array having a plurality oflight-emitting sources. Alternatively, it may be such a light sourcethat includes a light synthesis prism operative to synthesize beamsemitted from a plurality of semiconductor lasers.

The coupling lenses may match with the corresponding beams emitted fromthe semiconductor lasers one by one. Alternatively, one coupling lensmay couple two or more beams.

The cylindrical lenses may receive either a single incident beam orplural incident beams depending on the case.

The scanning lens B (scanning lens 206A) arranged in the scanningoptical system having the minimum angle (having an average incidentangle θA) between an incident beam to the deflector 4 and the opticalaxis of the scanning lens is determined to have a power in the sub scandirection proximate to the periphery at the incident beam side lowerthan a power in the sub scan direction proximate to the periphery at theopposite side. At least one scanning lens A (scanning lens 205A, 205A′)other than the scanning lens B has a sub scan curvature on at least onesurface asymmetrically varying gradually from the optical axis towardboth peripheries in the main scan direction.

The scanning lens A (scanning lens 205A, 205A′) is determined to have apower in the sub scan direction proximate to the periphery at theincident beam side higher than a power in the sub scan directionproximate to the periphery at the opposite side.

FIG. 10 may be considered as illustrating the portion at the right ofthe polygon mirror in the optical arrangement shown in FIG. 1 (in thiscase, the depicted optical system is symmetrically arranged about thepolygon mirror laterally). Alternatively, it may also be considered asillustrating two sets of the optical system of FIG. 10 arranged assuperimposed in the direction orthogonal to the figure. Also in FIG. 10,as for optical paths extending from the polygon mirror 204 to the targetsurfaces 208A and 208A′, they are shown as developed in the same planefor the convenience of depiction.

The semiconductor lasers 201A and 201A′ emit divergent beams, which areconverted into collimated beams (or weakly converged beams or weaklydiverged beams) through coupling optical systems including couplinglenses 202A and 202A′. The converted beams are then subjected to shapinginto desired beam sections while passing through apertures 214A and214A′ for forming desired spot diameters on the target surfaces. Theshaped beams then enter the cylindrical lenses 203A and 203A′ havingpowers only in the sub scan direction.

The beams emitted from the semiconductor lasers 201A and 201A′ have anopen angle θ in a deflecting rotation plane and a certain spacing in thesub scan direction (the direction perpendicular to the figure)therebetween. The cylindrical lenses 203A and 203A′ are arranged tocause the incoming beams to be condensed in the sub scan direction and,through a soundproof glass member 215, focused to line images extendinglonger in the main direction on the polygon mirror 204 in the vicinityof deflecting reflective surfaces thereof. When the beams are reflectedat the polygon mirror 204, they are converted into deflected beams thatdeflect at a constant angular velocity as the polygon mirror 204 rotatesat a constant velocity. The deflected beams pass through the soundproofglass member 215.

The beam emitted from the semiconductor laser 201A passes throughscanning lenses 205A and 206A and a dust-tight glass member 207A whiledeflecting and reaches as a condensed light spot onto the target surface208A for optically scanning the target surface 208A between locations HAand HA1. The beam emitted from the semiconductor laser 201A′ passesthrough scanning lenses 205A′ and 206A′ and a dust-tight glass member207A′ while deflecting and reaches as a condensed light spot onto thetarget surface 208A′ for optically scanning the target surface 8A′between locations HA′ and HA1′. A distance between a location H0 and thelocation HA1 as well as a distance between a location H and the locationHA′ is equal to 164 millimeters. A distance between the location H0 andthe location HA1′ as well as a distance between the location H and thelocation HA is equal to 150 millimeters. Similar to the embodiment ofFIG. 1, the deflected beams are, of course, received at photodetectors(not shown) for synchronization associated with the start of opticalscanning.

Specific examples of the optical scanner will be exemplified below.

In lens surface shapes in the following examples, a non-circular arcshape in the main scan plane (a virtual plan section parallel to themain scan direction including the optical axis of the lens) isrepresented by the following polynomial equation: $\begin{matrix}{X = {{\left( {Y^{2}/{Rm}} \right)/\left\{ {1 + \sqrt{1 - {\left( {1 + K} \right)\left( {Y/{Rm}} \right)^{2}}}} \right\}} + {A_{1} \cdot Y} + {A_{2} \cdot Y^{2}} + {A_{3} \cdot Y^{3}} + {A_{4} \cdot Y^{4}} + {A_{5} \cdot Y^{5}} + {A_{6} \cdot Y^{6}} + \ldots}} & (1)\end{matrix}$where Rm denotes a radius of curvature proximate to the axis in the mainscan plane at the optical axis; Y denotes a distance from the opticalaxis in the main scan direction; K denotes a conic constant; A₁, A₂, A₃,A₄, A₅, A₆ . . . denote higher-degree coefficients; and X denotes adepth in the optical axis direction. If one or more of odd-degreecoefficients A₁, A₃, A₅ . . . are “not equal to zero”, the non-circulararc shape given in equation (1) exhibits asymmetry in the main scandirection.

If the curvature in the sub scan direction (a curvature of the lens in avirtual plan section orthogonal to the main scan direction) varies inaccordance with a coordinate Y in the main scan direction, it isrepresented by the following polynomial equation:Cs(Y)={1/Rs(0)}+B ₁ ·Y+B ₂ ·Y ² +B ₃ ·Y ³ +B ₄ ·Y ⁴ +B ₅ ·Y ⁵+ . . .  (2)If one or more of odd-degree coefficients B₁, B₃, B₅ . . . are “notequal to zero”, the “curvature in the sub scan given” in equation (2)varies asymmetrically in the main scan direction.

A common axis non-sphericity can be represented by equation (1) using“R” replaced with the radius of curvature Rm.

EXAMPLE I

Example I shows a specific example of the optical scanner shown in FIG.1, which includes the following components: semiconductor lasers with anemission wavelength of 655 nanometers; coupling lenses with a focus of15 millimeters; cylindrical lenses with a focus of 70.2 millimeters; anda polygon mirror with six deflecting reflective surfaces and a diameterof 18 millimeters in an inscribed circle.

Shapes of first surfaces (surfaces facing the polygon mirror 4) of thescanning lenses 5A, 5A′, 5B, and 5B′ (having the same material andshape): Rm=−1030.23, Rs=−107.57, K=−4.041619E+02, A₄=6.005017E-08,A₆=−7.538155E-13, A₈=−4.036824E-16, A₁₀=4.592164E-20, A₁₂=−2.396524E-24,B₁=1.83062E-06, B₂=3.22511E-06, B₃=3.16208E-09, B₄=−4.21739E-10,B₅=−1.44343E-12, B₆=4.29602E-14, B₇=2.70172E-16, B₈=−6.80780E-18,B₉=−2.39731E-20, B₁₀=−3.80289E-21, B₁₁=8.81473E-25, B₁₂=4.40587E-25.

As the coefficients of the non-circular arc shape in the main scan planeinclude no odd-degree coefficients, the non-circular arc shape issymmetric about the optical axis in the main scan direction. As thecurvature in the sub scan direction includes odd-degree coefficients, itis asymmetric about the optical axis in the main scan direction.

In the above expression, for example, 8.81473E-25 means 8.81473×10⁻²⁵.This expression is similarly employed below.

Shapes of second surfaces of the scanning lenses 5A, 5A′, 5B, and 5B′:Rm=−109.082, Rs=−136.5, K=−5.427642E-01, A₄=9.539024E-08,A₆=4.882194E-13, A₈=−1.198993E-16, A₁₀=5.029989E-20, A₁₂=−5.654269E-24,B₂=−2.652575E-07, B₄=3.16538E-11, B₆=8.25027E-14, B₈=−1.05546E-17,B₁₀=−2.24388E-21, B₁₂=3.89635E-27.

In this surface, the non-circular arc shape in the main scan directionas well as the curvature in the sub scan direction is asymmetric aboutthe optical axis in the main scan direction.

Shapes of first surfaces of the scanning lenses 6A, 6A′, 6B, and 6B′(having the same material and shape): Rm=1493.654587, Rs=−70.715,K=5.479389E+01, A₄=−7.606757E-09, A₆=−6.311203E-13, A₈=6.133813E-17,A₁₀=−1.482144E-21, A₁₂=2.429275E-26, A₁₄=−1.688771E-30, B₂=−9.65043E-08,B₄=2.85907E-11, B₆=−1.94228E-15, B₈=2.66096E-20, B₁₀=1.95275E-24,B₁₂=−1.47642E-29.

Also in this surface, the non-circular arc shape in the main scandirection as well as the curvature in the sub scan direction isasymmetric about the optical axis in the main scan direction.

Shapes of second surfaces of the scanning lenses 6A, 6A′, 6B, and 6B′:Rm=1748.583900, Rs=−27.946, K=−5.488740E+02, A₄=−4.978348E-08,A₆=2.325104E-12, A₈=−7.619465E-17, A₁₀=3.322730E-21, A₁₂=−3.571328E-26,A₁₄=−2.198782E-30, B₁=7.27930E-07, B₂=4.77761E-07, B₃=−6.60302E-11,B₄=−4.19563E-11, B₅=9.09990E-15, B₆=2.25043E-15, B₇=−9.69556E-19,B₈=−1.52942E-20, B₉=4.19665E-23, B₁₀=−1.27596E-24, B₁₁=−2.48212E-28,B₁₂=4.34622E-29, B₁₄=−5.06733E-34.

In this surface, the non-circular arc shape in the main scan directionis symmetric about the optical axis in the main scan direction, and thecurvature in the sub scan direction is asymmetric about the optical axisin the main scan direction.

The scanning lenses 5A to 5B′ and 6A to 6B′ are composed of a materialwith a refractive index of 1.5273. The scanning lenses 5A to 5B′ and 6Ato 6B′ have thicknesses of 30 millimeters on the optical axis for thescanning lenses 5A to 5B′ and 8.5 millimeters for the scanning lenses 6Ato 6B′.

There are distances of 71.2 millimeters from the polygon mirror to thescanning lenses 5A to 5B′. There are distances of 66.5 millimeters fromthe scanning lenses 5A to 5B′ to the scanning lenses 6A to 6B′. Thereare distances of 157.8 millimeters from the scanning lenses 6A to 6B′ tothe target surfaces 8A to 8B′.

In the optical scanner of FIG. 1, when the optical system of Example Iis employed, average incident angles from the cylindrical lenses 3A to3B′ to the polygon mirror 4 are given below. (The average incidentangles are defined as incident angles to the deflecting reflectivesurfaces when a rotational angle of the polygon mirror 4 comes to themiddle between rotational angles corresponding to both outermostperipheries of an effective optical scanning width). That is, to Aoptical system (the optical system denoted with A-prefixed referencenumerals), B optical system (the optical system denoted with theB-prefixed reference numerals), A′ optical system (the optical systemdenoted with the A′-prefixed reference numerals) and B′ optical system(the optical system denoted with the B′-prefixed reference numerals),they are given as:

A optical system (B optical system): 57.1 degrees

A′ optical system (B′ optical system): 74 degrees

The locations of incident beams to the polygon mirror 4 areappropriately spaced from each other between A optical system and A′optical system as well as between B optical system and B′ opticalsystem. This enables A-B′ optical systems to have a substantiallyuniform effective optical scanning width to form images in a widerrange.

A′ optical system and B′ optical system have such lenses that are sameas the scanning lenses 6A and 6B but rotated 180 degrees about theoptical axis relative to the arrangement in A and B optical systems.Accordingly, A and A′ optical systems have such scanning lensesproximate to target surfaces that are same in shape as but different in“arrangement shape” from those of B and B′ optical systems. (As thecurvature in the sub scan direction on the second surface asymmetricallyvaries about the optical axis, arrangement shapes rotated 180 degreesabout the optical axis are different from each other).

FIGS. 11A and 11B illustrate image surface curvatures in A and A′optical systems according to Example I. The dashed line indicates theimage surface curvature in the main scan, and the solid line indicatesthe image surface curvature in the sub scan (like in the examplesdescribed later).

In Example I, a surface with a curvature in the sub scan directionasymmetrically varying about an optical axis in the main scan directionis employed as a first surface of the scanning lens 5A to 5B′ proximateto the polygon mirror 4. In addition, the scanning lenses 6A and 6B inA′ (B′) optical system is rotated 180 degrees about the optical axisrelative to the arrangement in A (B) optical system. This is effectiveto correct the image surface curvature well in A (B) optical system aswell as A′ (B′) optical system.

The scanning lens 6A to 6B′ proximate to the target surface has a powerin the sub scan direction higher than a power in the sub scan directionof a scanning lens 5A to 5B′ proximate to the polygon mirror 4. This iseffective to lower the absolute value of the lateral power of thescanning optical system in the sub scan direction. The lateral power ofthe scanning optical system in the sub scan direction, β, is −0.89,indicating that the scanning optical system is a reducing opticalsystem.

EXAMPLE II

Example II shows a specific example of the optical system in the opticalscanner of FIG. 1 similar to Example I.

A (B) optical system is similar to that in Example I. In A′ (B′) opticalsystem, an average incident angle to the polygon mirror 4 is equal to65.5 degrees. A′ (B′) optical system has a radius of curvature in thesub scan direction in the scanning lenses 6A′ and 6B′, which isdifferent from that in Example I. Therefore, the scanning lenses 6A and6A′ proximate to the target surfaces have different shapes from those ofthe scanning lenses 6B and 6B′.

Shapes of first surfaces of the scanning lenses 6A′ and 6B′:Rm=1493.654587, Rs=−70.715, K=5.479389E+01, A₄=−7.606757E-09,A₆=−6.311203E-13, A₈-6.133813E-17, A₁₀=−1.482144E-21, A₁₂=2.429275E-26,A₁₄=−1.688771 E-30, B₂=−9.65043E-08, B₄=2.85907E-11, B₆=−1.94228E-15,B₈=2.66096E-20, B₁₀=1.95275E-24, B₁₂=−1.47642E-29.

Also in this surface, the non-circular arc shape in the main scandirection as well as the curvature in the sub scan direction isasymmetric about the optical axis in the main scan direction.

Shapes of second surfaces of the scanning lenses 6A′ and 6B′:Rm=1748.583900, Rs=−27.946, K=−5.488740E+02, A₄=−4.978348E-08,A₆=2.325104E-12, A₈=−7.619465E-17, A₁₀=3.322730E-21, A₁₂=−3.571328E-26,A₁₄=−2.198782E-30, B₂=4.77368E-07, B₄=−4.18273E-11, B₆=2.20541E-15,B₈=−1.02432E-20, B₁₀=−1.30710E-24, B₁₂=2.68096E-29.

Also in this surface, the non-circular arc shape in the main scandirection as well as the curvature in the sub scan direction issymmetric about the optical axis in the main scan direction.

The scanning lenses 5A to 5B′ and 6A to 6B′ are composed of a materialwith a refractive index of 1.5273. The scanning lenses 5A to 5B′ and 6Ato 6B′ have thicknesses of 30 millimeters on the optical axis for thescanning lenses 5A to 5B′ and 8.5 millimeters for the scanning lenses 6Ato 6B′.

There are distances of 71.2 millimeters from the polygon mirror to thescanning lenses 5A to 5B′. There are distances of 66.5 millimeters fromthe scanning lenses 5A to 5B′ to the scanning lenses 6A to 6B′. Thereare distances of 157.8 millimeters from the scanning lenses 6A to 6B′ tothe target surfaces 8A to 8B′.

FIG. 12 illustrates an image surface curvature in A′ (B′) opticalsystem, which is corrected well together with the image surfacecurvature in A (B) optical system shown in FIGS. 11A and 11B.

The following Examples III and IV are examples according to theembodiment shown in FIGS. 6A and 6B. The semiconductor lasers 101A to101D emit laser beams with a wavelength of 780 nanometers. The couplinglenses 102A to 102D arranged to couple the beams emitted from the lightsources include positive lenses with a focus of f=15 millimeters, whichconvert the beams from the light sources into weak convergent beams.

In Examples III and IV, the coupled weak convergent beams are designedto be naturally focused (focused in accordance only with the convergenceof the weak convergent beams) on a position 1200 millimeters apart fromthe deflecting reflective surface of the polygon mirror 104 toward thetarget surface. Depending on design conditions, of course, the coupledbeams may be converted into either collimated beams or weak divergentbeams.

The beams passed through the coupling lenses 102A to 102D arebeam-shaped through the apertures 114A to 114D. Then, they are convertedinto line images extending longer in the main scan direction formed inthe vicinity of the deflecting reflective surface of the polygon mirror104 (with a radius of an inscribed circle: 18 millimeters) through thecylindrical lenses 103A to 103D having powers only in the sub scandirection.

The beams deflected at the polygon mirror 104 are guided through thescanning lenses 105 and 106A to 106D contained in the scanning opticalsystems to the target surfaces (photosensitive drums) 108A to 108D toform light spots for optical scanning of the target surfaces. There isan optical path length of 175 millimeters from the original point ofdeflection on the deflecting reflective surface to the focused positionat an image height of zero on the target surface.

EXAMPLE III

The following data is related to the cylindrical lenses 103A to 103Dthrough the target surfaces 108A to 108D. Similar to Examples I and II,Rm denotes the radius of curvature in the main scan direction; Rsdenotes the radius of curvature in the sub scan direction; D denotes aninterval between surfaces; and N denotes a refractive index of amaterial at a use wavelength. SURFACE NUMBER Rm Rs D N NOTE 1 ∞ 13.88 31.5244 cylindrical lens 2 ∞ ∞ 25 1 3 ∞ ∞ 33.3 1 deflecting reflectivesurface 4(*) 160.4 ∞ 13.5 1.5244 scanning lens 105 5(*) −141.3 ∞ 84.2 16(**) −700 −70 3 1.5112 scanning lenses 106A to 106D 7(***) −700 −15.641 1 8 — — target surface

The surfaces (fourth and fifth surfaces) denoted with the (*)-suffixednumbers have non-circular arc shapes in the main scan direction. Theyare “surfaces having no power in the sub scan direction” over the wholeeffective region. The non-circular arc shape is represented by equation(1). These fourth and fifth surfaces have the following shape data.FOURTH FIFTH SURFACE SURFACE K −60 4.693 A₄ −9.465E−07 −1.015E−06 A₆3.847E−10 2.438E−10 A₈ −8.113E−14 −7.856E−14 A₁₀ 1.000E−17 2.797E−17

The surface (sixth surface) denoted with the (**)-suffixed number has acircular arc shape in the main scan direction and a constant radius ofcurvature in the sub scan direction over the whole effective region.

The surface (seventh surface) denoted with the (***)-suffixed number hasa circular arc shape in the main scan direction, and a radius ofcurvature in the sub scan direction, which can be represented by:Rs(Y)=Rs+a2·Y ² +a4·Y ⁴ +a6·Y ⁶  (3)where Rs denotes a radius of curvature at Y=0; and a2, a4, and a6 denotecoefficients, which have the following respective values:

a2=6.3E-04, a4=a6=0

The seventh surface has a radius of curvature, Rs(Y), in the sub scansection that varies along a secondary curve in accordance with a lensheight, Y, in the main scan direction. This shape enables the imagesurface curvature to be well corrected in the sub scan direction.

The optical system of Example III may be employed in the optical scannerof FIGS. 6A and 6B. In this case, with respect to A optical system (theoptical system denoted with A-prefixed reference numerals in FIGS. 6Aand 6B) and D optical system (the optical system denoted with theD-prefixed reference numerals in FIGS. 6A and 6B), image surfacecurvatures are shown in FIGS. 13A and 13B. A optical system has anaverage incident angle of 60 degrees to the polygon mirror 104. Doptical system has an average incident angle of 76.9 degrees to thepolygon mirror. The average incident angle increases by 5.43 degrees peroptical system from A optical system through D optical system.

Despite the presence of a large difference of 16.9 degrees in incidentangle between A optical system and D optical system, the image surfacecurvatures can be well corrected. Also in B optical system and C opticalsystem, the image surface curvatures can be well corrected though theyare not depicted.

The optical scanning system is a reducing optical system with a lateralpower β of −0.316 in the sub scan direction. This is effective to lowerthe effect of the sag on the polygon mirror 104 and reduce the imagesurface curvature in the sub scan.

EXAMPLE IV

This example is similar to Example III except that lens data about thescanning lenses 105 and 106A to 106D contained in the optical scanningsystem is altered as follows: SURFACE NUMBER Rm Rs D N NOTE 1 ∞ 13.88 31.5244 cylindrical lens 2 ∞ ∞ 25 1 3 ∞ ∞ 33.3 1 deflecting reflectivesurface 4(*) 160.4 −100 13.5 1.5244 scanning lens 105 5(*) −141.3 −13584.2 1 6(**) −700 −70 3 1.5112 scanning lenses 106A to 106D 7(***) −700−15.6 41 1 8 — — target surface

The fourth and the fifth surfaces denoted with the (*)-suffixed numbershave non-circular arc shapes in the main scan direction and negativepowers in the sub scan direction.

The non-circular arc shape in the main scan direction expressed inequation (1) has the following coefficients: FOURTH FIFTH SURFACESURFACE K −60 4.693 A₄ −9.465E−07 −1.015E−06 A₆ 3.847E−10 2.438E−10 A₈−8.113E−14 −7.856E−14 A₁₀ 1.000E−17 2.797E−17

The shape in the sub scan direction can be expressed in equation (3)where the coefficients a2, a4, and a6 have the following values: FOURTHFIFTH SURFACE SURFACE a2 −6E−02 0 a4 0 0 a6 0 0

Only in the fourth surface, the radius of curvature in the sub scandirection varies in accordance with the lens height Y in the main scandirection. Thus, it is possible to well correct the curved opticalscanning line even if positions in the sub scan direction of the beamspassing through the scanning lens 105 differ in accordance with thetarget surfaces to be optically scanned. This is effective to reduce therelative positional deviations of beams in the sub scan direction.

The sixth surface denoted with the (**)-suffixed number has a circulararc shape in the main scan direction and a constant radius of curvaturein the sub scan direction over the whole effective region.

The seventh surface denoted with the (***)-suffixed number has acircular arc shape in the main scan direction, and a radius of curvaturein the sub scan direction that can be represented by equation (3) withcoefficients of the following values:

a2=−6.3E-04, a4=a6=0

The seventh surface has a radius of curvature in the sub scan sectionthat varies along a secondary curve in accordance with a lens height Yin the main scan direction. This shape enables the image surfacecurvature to be well corrected in the sub scan direction.

The scanning optical system in Example IV has a lateral power β of−0.311 in the sub scan direction, which has a further reduced absolutevalue of the power compared to Example III. This is effective to wellcorrect the image surface curvature in the sub scan and achieve a smalland stable spot diameter.

In some additional explanation, the single beam mode is applied foroptical scanning of the target surfaces in the above-described exampleswhile the multi-beam mode may also be applied. The scanning lenses inthe examples are composed of easily processible molded resins.Alternatively, they may include glass lenses.

In all examples, the scanning lenses corresponding to different targetsurfaces are designed to have the same shape in the main scan direction.This is effective to reduce relative “dot positional deviations” in themain scan direction on the different target surfaces.

EXAMPLE V

Example V exemplified below is a specific example with respect to theoptical system in the optical scanner explained with reference to FIG.10, which includes the following components: semiconductor lasers with awavelength of 655 nanometers; coupling lenses with a focus of 27millimeters (collimator lenses); cylindrical lenses with a focus of 70.2millimeters; a polygon mirror with five deflecting reflective surfacesand a diameter of 18 millimeters in an inscribed circle; and averageincident angles of θA=58 degrees and θA′=73 degrees.

Shapes of first surfaces (surfaces facing the polygon mirror 204) of thescanning lenses 205A and 205A′ (having the same material and shape):Rm=−279.9, Rs=−61, K=−2.900000+01, A₄=1.755765E-07, A₆=−5.491789E-11,A₈=1.087700E-14, A₁₀=−3.183245E-19, A₁₂=−2.635276E-24, B₁=−2.066347E-06,B₂=5.727737E-06, B₃=3.152201E-08, B₄=2.280241E-09, B₅=−3.729852E-11,B₆=−3.283274E-12, B₇=1.765590E-14, B₈=1.372995E-15, B₉=−2.889722E-18,B₁₀=−1.984531E-19.

A shape of a second surface of the scanning lenses 205A (205A′):Rm=−83.6, K=−0.549157, A₄=2.748446E-07, A₆=−4.502346E-12,A₈=−7.366455E-15, A₁₀=1.803003E-18, A₁₂=2.727900E-23.

The scanning lenses 206A and 206A′ (having the same material and shape).

A shape of a first surface of the scanning lens 6A (the average incidentangle: θA=58 degrees): Rm=6950, Rs=110.9, K=0.000000+00,A₄=1.549648E-08, A₆=1.292741E-14, A₈=−8.811446E-18, A₁₀=−9.182312E-22,B₁=−9.593510E-07, B₂=−2.135322E-07, B₃=−8.079549E-12, B₄=2.390609E-12,B₅=2.881396E-14, B₆=3.693775E-15, B₇=−3.258754E-18, B₈=1.814487E-20,B₉=8.722085E-23, B₁₀=−1.340807E-23.

A shape of a first surface of the scanning lens 206A′ (the averageincident angle: θA′=73 degrees): Rm=6950, Rs=110.9, K=0.000000+00,A₄=1.549648E-08, A₆=1.292741E-14, A₈=−8.811446E-18, A₁₀=−9.182312E-22,B₁=−9.593510E-07, B₂=−2.135322E-07, B₃=8.079549E-12, B₄=2.390609E-12,B₅=−2.881396E-14, B₆=3.693775E-15, B₇=3.258754E-18, B₈=1.814487E-20,B₉=−8.722085E-23, B₁₀=−1.340807E-23.

Shapes of second surfaces of the scanning lenses 206A and 206A′ (commonfor the average incident angles: θA=58 degrees, θA′=73 degrees): Rm=766,Rs=−68.22, K=0.000000+00, A₄=−1.150396E-07, A₆=1.096926E-11,A₈=−6.542135E-16, A₁₀=1.984381E-20, A₁₂=−2.411512E-25, B₂=3.644079E-07,B₄=−4.847051E-13, B₆=−1.666159E-16, B₈=4.534859E-19, B₁₀=−2.819319E-23.

All scanning lenses have a refractive index of 1.52724 at a wavelengthof 655 nanometers.

A distance between the deflecting reflective surface and the firstsurface of the scanning lens 205A (205A′): d1=64 millimeters.

A thickness at the center of the scanning lens 205A (205A′): d2=22.6millimeters.

A distance between the second surface of the scanning lens 205A (205A′)and the first surface of the scanning lens 206A (206A′): d3=75.9millimeters.

A thickness at the center of the scanning lens 206A (206A′): d4=4.9millimeters.

A distance between the second surface of the scanning lens 206A (206A′)and the target surface 208A, 208A′: d5=158.7 millimeters.

The dust-tight glass members 207A, 207A′ and the soundproof glass member215 have a refractive index of 1.514 and a thickness of 1.9 millimeters.The soundproof glass member 215 tilts at 10 degrees to the directionparallel to the main scan direction in the deflecting rotation plane.

FIGS. 14A, 14B, 15A, 15B, 16A, and 16B illustrate aberration diagrams ofimage surface curvature on the left (with the solid line: Sub scan, andthe dotted line: Main scan) and Constant velocity characteristic on theright (with the solid line: Reality, and the dotted line: fθcharacteristic).

FIGS. 14A and 14B illustrate image surface curvatures with the incidentangle of 58 degrees. FIGS. 15A and 15B illustrate image surfacecurvatures with the incident angle of 73 degrees. FIGS. 16A and 16Billustrate image surface curvatures with the incident angle of 73degrees and the scanning lens 206A′ arranged as rotated 180 degreesaround the optical axis. It is possible to correct for the sag-effecteddeterioration of the image surface curvature in the sub scan, which isotherwise caused when the scanning lens 206A′ is not rotated 180 degreesas shown in FIGS. 15A and 15B.

FIGS. 17A, 17B, 18A, and 18B are diagrams illustrating variations inspot diameter in the main scan direction due to defocus according toExample V. FIGS. 19 and 20 are diagrams illustrating power of thescanning lenses 205A (205A′) and 206A (206A′) in the sub scan direction.FIGS. 21 and 22 are diagrams illustrating variations in sub scancurvature in the main scan direction on the first surfaces of thescanning lenses 205A (205A′) and 206A (206A′) of the scanning lens inExample V.

As obvious from these diagrams, the optical system in Example V has anexcellent performance.

Through the use of the optical scanner that employs the optical systemin Example V, the image forming apparatus as shown in FIG. 9 can beconfigured, needless to say.

Although the invention has been described with respect to a specificembodiment for a complete and clear disclosure, the appended claims arenot to be thus limited but are to be construed as embodying allmodifications and alternative constructions that may occur to oneskilled in the art which fairly fall within the basic teaching hereinset forth.

1. An optical scanner comprising: a plurality of light sources; acoupling optical system arranged to couple beams emitted from the lightsources; a line image focusing optical system arranged to focus thebeams coupled through the coupling optical system to a line imageextending longer in a main scan direction; a deflector that hasdeflecting reflective surfaces in the vicinity of focused positions ofthe line image and arranged to deflect the beams from the line imagefocusing optical system; and a plurality of scanning optical systemsarranged to guide the beams deflected at the deflector to differenttarget surfaces to form focused light spots, wherein the deflector has acommon rotary axis for deflecting reflective surfaces, the beamsentering a common deflecting reflective surface of the deflector totravel toward different target surfaces has an open angle θ in adeflecting rotation plane, each of the scanning optical systems includesat least two scanning lenses and corresponding scanning lenses in thescanning optical systems are identical, and wherein at least onespecific scanning lens in the scanning optical systems arranged to guidethe beams deflected at the common deflecting reflective surface todifferent target surfaces is located at a position 180 degrees rotatedabout an optical axis from a corresponding specific scanning lens inanother scanning optical system, and wherein the specific scanning lenshas a sub scan curvature on at least one surface with a shapeasymmetrically varying gradually from an optical axis toward bothperipheries in the main scan direction.
 2. The optical scanner accordingto claim 1, wherein the specific scanning lens arranged in the scanningoptical systems having the minimum angle between an incident beam to thedeflector and the optical axis of the scanning lens is determined tohave a power in the sub scan direction at incident beam side proximateto a periphery lower than a power in the sub scan direction at oppositeside proximate to the periphery.
 3. The optical scanner according toclaim 1, wherein at least one scanning lens other than the specificscanning lens has a sub scan curvature on at least one surfaceasymmetrically varying gradually from an optical axis toward bothperipheries in the main scan direction.
 4. The optical scanner accordingto claim 3, wherein the scanning lens other than the specific scanninglens is determined to have a power in the sub scan direction at incidentbeam side proximate to periphery higher than a power in the sub scandirection at opposite side proximate to the periphery.
 5. An imageforming apparatus for multicolor, comprising an optical scanner thatincludes a plurality of light sources; a coupling optical systemarranged to couple beams emitted from the light sources; a line imagefocusing optical system arranged to focus the beams coupled through thecoupling optical system to a line image extending longer in a main scandirection; a deflector that has deflecting reflective surfaces in thevicinity of focused positions of the line image and arranged to deflectthe beams from the line image focusing optical system; and a pluralityof scanning optical systems arranged to guide the beams deflected at thedeflector to different photosensitive objects to form focused lightspots, wherein the deflector has a common rotary axis for deflectingreflective surfaces, the beams entering a common deflecting reflectivesurface of the deflector to travel toward different photosensitiveobjects has an open angle θ in a deflecting rotation plane, each of thescanning optical systems includes at least two scanning lenses andcorresponding scanning lenses in the scanning optical systems areidentical, and wherein at least one specific scanning lens in thescanning optical systems arranged to guide the beams deflected at thecommon deflecting reflective surface to different photosensitive objectsis located at a position 180 degrees rotated about an optical axis froma corresponding specific scanning lens in another scanning opticalsystem, and wherein the specific scanning lens has a sub scan curvatureon at least one surface with a shape asymmetrically varying graduallyfrom an optical axis toward both peripheries in the main scan direction.